worthington, stephen r. h. hydraulic and geological factors influencing conduit flow depth

8/11/2019 Worthington, Stephen R. H. Hydraulic and Geological Factors Influencing Conduit Flow Depth

1/19

Speleogenesis and Evolution of Karst AquifersThe Virtual Scientific Journal

ISSN 1814-294X

www.speleogenesis.info

Hydraulic and geological factors influencing conduit flow depth

Stephen R H Worthington

Worthington Groundwater, 55 Mayfair Avenue, Dundas, Ontario, L9H 3K9, Canada.E-mail: [email protected]

Re-published from: Cave and Karst Science, 31 (3), 2004, 123-134.

Abstract

There has much been speculation as to whether cave formation should occur at, above, or below the water table, but a satisfactory

explanation has been lacking until recently. The last 50 years has seen extensive mapping of caves both above and, more recently,

below the water table. It is now becoming apparent that there are systematic differences in depth of flow between different areas and

that conduit flow to depths >100m below the water table is not uncommon. Such deep flow is facilitated by the lower viscosity of

geothermally heated water at depth. Analysis of data from caves shows that depth of flow is primarily a function of flow path length,

stratal dip and fracture anisotropy. This explains why conduits form at shallow depths in platform settings such as in Kentucky, at

moderate depths (10100m) in folded strata such as in England and in the Appalachian Mountains, and at depths of several hundred

metres in exceptional settings where there are very long flow paths.

Keywords: Speleogenesis, conduit flow, deep flow

Introduction

The nature and extent of cave development with

respect to the water table has received much

attention, especially in the first half of the

Twentieth Century (Lowe, 2000a). Early theories

were largely speculative because few caves above

the water table and none below the water table had

been accurately mapped. For instance, in 1950 there

were only seven caves with mapped lengths greater

than 10km. In the last 50 years, however, this

number has grown rapidly, reaching 125 in 1977

and 350 in 2000 (Chabert, 1977; Madelaine, 2001).

The growth of mapped cave passages below the

water table is even more marked. In 1950

underwater exploration in caves had barely

commenced, but by 2000 there were 14 caves

explored to depths of at least 150m below the water

table (Farr, 2000). This impressive dataset of

mapped caves provides an invaluable empirical

database for ideas on cave development.

Conduit development results from the interplay

between hydraulic, chemical and geological factors.Early calculations on conduit enlargement were

disappointing as they showed that infiltrating water

would quickly become saturated with respect to

calcite, that no further dissolution would then take

place, and thus caves could not be formed (Weyl,

1958). Caves clearly do exist, and so some

alternative explanations were proposed, such as the

presence of sulphides (Howard, 1964) or the

occurrence of mixing corrosion (Bgli, 1964). At

the time it thus appeared that caves might only form

in some special situations and so be rare. However,

this concept was overturned in the 1970s when lab

experiments showed that the dissolution rate ofcalcite and of dolomite is non-linear and that there

is a large reduction in the rate as chemical

equilibrium is approached (Berner and Morse,

1974; Plummer and Wigley, 1976; Herman and

White, 1985). These results were in turn

incorporated into numerical models, which showed

that caves form in all unconfined carbonate aquifers

(Dreybrodt, 1990; Palmer, 1991). Furthermore, this

process occurs not only where there is sinking

stream recharge but also where there is percolation

recharge (Dreybrodt, 1996).

Early studies on the depth of cave development

with respect to the water table focused largely on

hydraulic factors. For instance, Davis (1930) noted


2/19

S.R.H.Worthington/ Speleogenesis and Evolution of Karst Aquifers, 2005, 3 (1), p.2

that some flow lines from recharge areas to

discharge areas describe arcs deep below the water

table during the initial pre-karstification stage of

flow through an aquifer, and he suggested that cave

development could occur along such deep flow

paths. Swinnerton (1932) suggested that the

greatest flow and thus the greatest dissolution

would occur along the shortest flow path, that

shallow flow paths are the shortest, and

consequently that conduit formation close to the

water table is favoured. Thrailkill (1968) analysed

flow through shallow and deep flow paths and his

findings supported Swinnerton (1932). The concept

of cave development close to the water table

attracted widespread support and the occurrence of

deep phreatic flow presented a challenge because

there was no known process that explained it. Ford

and Ewers (1978) proposed that deep flow onlyoccurs where there are a limited number of open

fractures and that it is solely the presence of these

open fractures that facilitates conduit development

deep below the water table. However, Worthington

(2001) carried out a comprehensive analysis of the

equation for laminar flow through fractures and

showed that the effect of geothermal heating results

in increased flow for deep flow paths.

Consequently, the presence of random large open

fractures at depth is not required to explain deep

flow.

The most widely quoted model in recent yearshas been that of Ford and Ewers (1978), which

appeared to provide a comprehensive explanation

of the occurrence of deep phreatic, shallow phreatic

and water table caves. However, there has been a

general failure to find examples that fit the model,

and Ford (2000) stated that the model does not

attempt to predict what will be the effective fissure

frequency and aperture in any particular

topographic or geologic setting. This raises the

spectre that cave development might occur at

unpredictable depths below the water table, being

related only to randomly located open fractures.

This pessimistic view of cave formation appears

to be contradicted by the growing evidence from

cave exploration and mapping that there are

systematic differences between different areas in

the depth of flow. For instance, cave diving in the

Mendips, the Peak District and in the Yorkshire

Dales has shown that these three areas in England

have sumps that descend to as much as several tens

of metres below the water table (Farr, 2000).

Geomorphological studies in English caves have

demonstrated that some fossil conduits had similardepths of flow (Ford, 1968; Waltham, 1974). In

contrast, extensive cave exploration in Kentucky

indicates that few conduits were formed more than

a few metres below the water table (Palmer, 1987),

whereas in some mountainous areas there are

examples of conduits formed at depths >100m

below the water table (Waltham and Brook, 1980;

Smart, 1984; Farr, 2000, Jeannin et al., 2000;

Yonge, 2001).

The systematic differences between England,

Kentucky and mountainous areas suggest that depth

of flow is likely to be a function of one or more

parameters that vary between these three settings.

Worthington (2001) found that depth of flow was a

function of stratal dip and flow path length, but

only a limited number of parameters was

considered in that study. The discussion below

considers a larger number of parameters that might

influence the depth of conduit flow, including

hydraulic factors, fracture permeability, fracturegeometry, spacing of bedding planes, and

topography.

Hydraulic factors

Flow along fractures in the early stages of

karstification is in the laminar regime, and can be

described by the Hagen-Poiseuille equation (White,

1988, p.162). This describes head loss (h) through a

circular pipe as

h= 8 !v L/ ("gr2) (1)

where ! is dynamic viscosity, " is the density of

water, vis velocity,Lis conduit length, ris conduit

radius, andgis the acceleration due to gravity.

Thrailkill (1968) calculated the differences

between shallow and deep flow paths in

horizontally-bedded strata by using Equation 1. His

results showed that shallow flow is slightly greater

than deep flow, implying that conduits should

develop close to the water table. However,

Thrailkill used the simplifying assumption of

constant temperature and constant viscosity in hiscalculations.

The average global geothermal gradient is about

25C/km, so that water following a deep flow path

in a limestone aquifer will be slightly warmer than

water following a shallower flow path. The density

and dynamic viscosity of water both vary as a

function of temperature, and can be combined to

give the kinematic viscosity, which decreases by

50% between 10C and 40C. This results in

increased flow in fractures at depth, increased

dissolution, and an environment for preferentialformation of conduits deep below the water table.


3/19


Fig. 1.Relative flow in shallow and deep conduits inflat-bedded limestone where the length/depth ratio is

100. A) Greater flow in the shallow conduit where theflow path is 1km long due to the shorter flow path in the

shallow conduit. B) Greater flow in the deep conduitwhere the flow path is 10km long, due to the lesser

viscosity at depth. C) Greater flow in the shallowerconduit where initial apertures in the horizontal fracturesare twice the apertures in the vertical fractures.

Fig. 1 shows a comparison of flow through

shallow and deep flow paths, where the temperature

at the water table is 20C and the geothermal

gradients is 25C/km. A single input and single

output are modelled, with flow through a shallow

and a deep conduit. This is similar to the model of

Thrailkill (1968), except that all terms in the HagenPoiseuille equation are considered here. Three cases

are examined in Fig. 1 and in all cases the deep

flow path is 2% longer than the shallow flow path.

Figures 1a and 1b are for isotropic conditions,

where the apertures of the horizontal and vertical

pipes are the same.

For a short (1km) flow path the lower viscosity

at depth does not compensate for the longer flow

path, so flow through the shallow pipe is greater

(Figure 1a). However, the opposite is true for the

longer (10km) flow path in Fig. 1b, with more flowpassing through the deeper conduit. Worthington

(2001) calculated that a distance of 3300m is the

critical flow path length threshold for more efficient

flow path at depth, assuming a geothermal gradient

of 25C/km and that the strata are flat-lying. Fig.1c

shows results for anisotropic conditions, where the

initial apertures of the horizontal pipes are twice

that of the vertical pipes. The anisotropy results in

greater flow through the shallow pipe.

The hydraulic analysis shows that deep conduit

development should be favoured in many settings,

implying that the base of a limestone aquifer is the

optimum location for conduits. In fact, such a

location for conduits is rare (excepts for conduits

formed in the vadose zone), implying that there

must be other pertinent factors that favour shallow

flow or inhibit deep flow. One possibility is

anisotropy (Fig. 1c), and the evidence for this is

discussed next.

Fracture permeability

Evidence of fracture permeability from cave maps

and flow path analysis

Conduits developed in older (e.g. Palaeozoic)

limestones are almost all oriented along bedding

planes, joints, or faults, or along intersections of

two of these fracture planes. Jameson (1985) found

that the initial fracture guidance for a passage could

best be inferred in caves where the fractures are

prominent but widely spaced, bedding is massive,roof collapse is minimal, sedimentation is limited,

and passage size is not so great that traces of the

initial guiding fractures have been eroded away.

Few caves fit all these conditions and so it is

commonly difficult to identify the initial guiding

fractures. Furthermore, few detailed studies of

fracture guidance in caves have been made. One

such study is by Jameson (1985), who found that all

but 2% of the passage length in part of Friars Hole

System, West Virginia, was formed along fractures.

Matrix permeability is higher in younger

limestones and so fracture-guided conduits may be

less important in some of these rocks. Nevertheless,

in the limestones of Eocene to Miocene age at Mulu

there is widespread passage development along

bedding planes, joints and faults (Waltham and

Brook, 1980). Furthermore, many cave passages in

early Cainozoic limestones in Tonga and late

Cainozoic limestones in the Bahamas are oriented

along near-vertical fractures (Lowe and Gunn,

1986; Palmer, 1986).

The alignment of cave passages along bedding

planes, joints and faults gives an indication of therelative permeability of these features. Mammoth

Cave, Friars Hole System and Castleguard Cave


4/19


provide examples of fracturing (Figures 25), and

these caves have been widely cited in the literature

(Gunn, 2004; Culver and White, 2005).

Mammoth Cave, Kentucky, is the worlds

longest cave and has figured prominently in

discussions of cave formation. It is located in alow-dip mid-continent setting where there is little

faulting or folding. Joints in the cave are sparse,

individual joints have very limited vertical and

horizontal extents, and few passages have clear

joint orientation (Deike, 1989; Palmer, 1989a,b). In

this situation, almost all passages follow bedding

planes and in plan view have meandering paths

(Fig. 2). Swinnerton Avenue provides a typical

example. All of the approximately 1000m of

passage is aligned along bedding planes except for

a 3m section where flow rose on a joint (Fig. 3).

Scuba diving in the Mammoth Cave area has shown

that most active phreatic passages are located

within a few metres of the water table. Likewise,

studies of fossil passages indicate that most were

within a few metres of the water table when they

were active (Palmer, 1987, 1989a,b). The scarcity

of clear passage guidance on either joints or faults

and the frequent large width/height ratios of

phreatic passages at Mammoth Cave indicate that

the initial horizontal hydraulic conductivity (Kh)

along bedding planes was much greater than the

initial vertical hydraulic conductivity (Kz) along

joints or faults.

Fig. 2.Relationship of cave passages in part of the Mammoth Cave System to the surface outcrops of limestonealong valleys (after cave map by Cave Research Foundation and geology map by U.S. Geological Survey).

Fig. 3.Profile of part of Swinnerton Avenue in the Mammoth Cave System (after Palmer, 1989a).


5/19


Fig. 4.Map of Friars Hole System,

showing limestone inliers whererecharge to the cave occurs

(based on map compiled by D.Medville).

Friars Hole System, West Virginia, provides a

second example (Fig. 4). The cave is the longest in

the Appalachian Mountains. It lies close to the

boundary between the Appalachian Plateau and

Valley and Ridge Provinces, and the structure

shows features of both geological provinces. The

entrances to the cave lie along a valley, Friars Hole,where a series of limestone inliers have been

exposed. Sinking streams typically descend

downdip to the northwest through the vadose zone

in the upper 50m of limestone, and then along

almost horizontal base-level passages along the

strike to the southwest. Many of these base-level

passages are formed at the intersection of low-angle

thrust faults and the contact between the Union

Limestone and the underlying Pickaway Limestone

(Worthington, 1984; Worthington and Medville,

2005). The detailed study by Jameson (1985) of

429m of passage in Snedegars Cave showed that37% of the passage was oriented along bedding

planes, 30% on joints, 20% on bed/joint

intersections, 7% on faults, 4% on fault/joint

intersections, and the remaining 2% had no guiding

fracture. From a geomorphological study,

Worthington (2001) inferred that the mean depth of

flow in fossil conduits was 17m below the water

table. The roughly equal proportions of bedding

plane guidance and joint or fault guidance for

passages at Friars Hole System (Jameson, 1985), as

well as the elongation of phreatic passage cross-

sections along either bedding planes or on faults orjoints, indicates that the initial pre-dissolution

apertures f bedding planes were similar to those of

faults and major joints. Consequently, the initial

vertical and horizontal fracture permeabilities were

of similar magnitude (Kh=Kz).

The third example is Castleguard Cave, which is

the longest cave in Canada and is located in the

Rocky Mountains. The caves topographical and

geological situations are described by Ford et al.(2000). Fig. 5 shows the plan and profile of the

cave. The main passage extends updip for 8921m

from its entrance at 2010m above sea level to a

termination where it is blocked by glacier ice that

has intruded from the overlying Columbia Icefield.

The plan shows that the main passage is oriented

along a series of northwest-trending joints.

However, the profile shows that the cave was

almost all developed on three bedding planes (Fig.

5, profile). The lowest of these is followed by the

main passage for 7045m. The two pitches are

developed on joints or faults, and the remainder ofthe main passage is developed along bedding planes

(40% of the total length) or bed-joint intersections

(60%). The longest distance that a passage follows

a single bed-joint intersection is 650m. There has

been minor movement, possibly of just a few

centimetres, on both joint and bedding plane

fractures (Ford et al.,2000). The geomorphology of

the cave suggests that it was enlarged up to a cross-

section of about 3m2while it was below the water

table, indicating that the present entrance was more

than 370m below the water table at that time.

Passage cross-sections and fracture guidance

suggest thatKh=Kz.


6/19


Fig. 5.Plan (top) and profileprojected along the strike (bottom)of Castleguard Cave. The profileshows only the main passage (basedon survey compiled by S.

Worthington).

In Britain there have been many studies that have

described the major guiding fractures in caves, such

as in South Wales (e.g. Coase and Judson, 1977),

the Forest of Dean (e.g. Elliott et al., 1979), the

Mendip Hills (e.g. Drew, 1975), Derbyshire (e.g.

Ford, 1977) and Yorkshire (e.g. Waltham, 1974).

There are many cave passages oriented along joints

or faults close to sections of cave where faults and

joints have much less importance than bedding

planes in guiding cave passages. Leck Fell providesa notable example. The stream in Short Drop Cave

flows down the axis of a plunging syncline and is

perched 100m above the water table, indicating

narrow joints apertures in this area. However, just

200m to the north the deep shafts of Deaths Head

Hole, Rumbling Hole and Big Meanie are aligned

on a single vertical fault (Waltham, 1974; Waltham

and Hatherley, 1983), and this demonstrates the

local-scale variability inKh/Kz . None of the above

studies were carried out to the level of detail of

Jameson (1985), and so there are no statistics on therelative importance of the various types of fracture

or fracture intersections in providing guiding

pathways for passages.

Bedding planes are used extensively in all the

caves described above. However, joint and fault

guidance is extremely variable between caves. In

most cases bedding plane and joint or fault

apertures appear to be similar, giving an isotropic

fracture network (Kh = Kz). Less commonly the

fracture network may be anisotropic, with Kh> Kz

or Kh < K

z. Mammoth Cave is an example of the

former, whereKh> Kz, and this inhibits deep flow.

Deaths Head Hole is an example of the latter, with

Kh


7/19


Fig. 6 depicts an aquifer where flow from a

recharge area to a discharge area is in the same

direction as the stratal dip. Figure 6a shows a

simple initial flow field before the start of

dissolution. A single source of recharge is shown,

such as occurs where a sinking stream develops.

Initially, there are a series of flow lines from the

area of recharge to the area of discharge. The

following three figures (6b,c,d) show three

possibilities for where conduit enlargement might

occur. Fig. 6b shows a cave with six phreatic loops

and a flow path that follows a generally curving

pattern below the water table. Figure 6c also shows

six phreatic loops, but the conduit is in general

closer to the water table than in 6b. Figure 6d

shows a single phreatic loop. All three flow paths

have identical lengths, with the conduit following a

bedding plane for a horizontal distance of 1500mand following one or more joints vertically for a

total of 180m.

Given the equal length of the flow paths in

Figures 6b, 6c and 6d, it might be considered that

there are equal probabilities of a conduit forming

along any one of them. However, there are reasons

why each one of these flow paths might be

favoured. The flow path in Fig. 6b might be

favoured if the early conduit dissolution was along

a flow path similar to that in a porous medium and

if there is a balance between the two competing

factors of decreasing fracture aperture with depth

(which promotes shallow flow) and decreasing

viscosity with depth (which promotes deep flow).

The flow path in Fig. 6c might be favoured if

factors such as greater fracture apertures at shallow

depth or mixing corrosion between conduit water

and percolation were the most important factors.

The flow path in Fig. 6d is favoured if the fracture

network is isotropic as in Figure 1b.Fig. 7 shows the equivalent situation where flow

is along the strike. Fig. 7a shows flow lines along a

single bedding plane from a recharge area to a

discharge area and Figures 7b, 7c, and 7d show

three possibilities of where a conduit might form. It

is assumed that there are two major perpendicular

joint sets and that conduits form at the intersection

of joints with the bedding plane. The flow paths in

Figures 7b, 7c and 7d have identical lengths. The

reasons why one of these three might be favoured

for conduit development are the same as with the

downdip case (Fig. 6).

Fig. 8 shows a simplified rectilinear flow system

that is similar to Figure 1 but has flow along a

dipping bedding plane rather than a vertical

fracture. The length of the flow path P is

P = L + 2D/(sin !) (2)

where L is the horizontal distance of the flow path,

D is the depth of the conduit and !is the stratal dip

in degrees. Shallow dips have increasingly long

flow paths and thus there is a lower probability that

the more efficient flow at depth (q.v. Equation 1)will be associated with low dips. If the depth of

flow is inversely proportional to the increasing

length of the flow path then the depth of flow will

be proportional to the sine of the dip.

Fig. 9 shows two caves with flow paths that are

similar to Figures 6b and 7b, respectively. The flow

path between Grotte Annette and Trou de Glaz is

primarily downdip (Fig. 9a), and is one of the major

Fig.6(left). Potential flow paths where the flow path

from a sink to a spring is downdip. A) Initial flow field;B) D) Possible flow paths. The three flow paths in BD have identical lengths.


8/19


flow paths in this 50km-long cave (Lismonde,

1997; Audra, 2004). It was used as the basis for

Fig. 6, and the flow pattern is clearly very similar to

Fig. 6b. As discussed earlier, this suggests that the

pattern of preferential solution was influenced

principally by the initial flow field in combination

with decreasing fracture apertures with depth.

However, the geology also plays an important role.

The section of cave shown is developed in 190m of

Cretaceous limestones. Lismonde and Marchand

(1997) identified just five bedding planes within

this 190m section that are preferentially used for

conduit development, and most of the cave shown

in Figure 8a is aligned along one of these bedding

planes (Fig. 10). A relatively minor fraction of the

passages has vertical flow along joints or faults

(Fig. 11).

Fig. 7.Potential flow paths where the flow path from asink to a spring is along the strike and where conduitsform at the intersection of joints and a single beddingplane. A) Initial flow field; B) D) Possible flow paths.The three flow paths in BD have identical lengths. Thedipping bedding plane is assumed to extend to much

greater depths than is shown.

Fig. 8. A simple rectilinear flow path on a dipping beddingplane.

Fig. 9. Major conduit flow paths that exhibit a single

curving loop below a former water table. A) Profile ofdowndip flow in Dent de Crolles, France (adapted fromLismonde, 1997); B) Perspective view of 12km flowpath on strike at Siebenhengste (S), Fitzlischacht (F) and

the caves A2 and F1, Switzerland (adapted from Jeanninet al.,2000). Note: DZ = Deep Zone.


9/19


Fig. 10.Bedding plane guided phreatic tube in Trou deGlaz. The passage was formed at least 50m below the

water table.

Fig. 11.Joint-guided rift in Trou de Glaz that wasformed by upward flow at least 60m below the watertable.

Figure 9b shows the caves of the Siebenhengste

area in Switzerland that developed when the water

table was at 1440m asl. Most of the passages are

developed at the base of the Schrattenkalk

Formation, a pure limestone that is 150200m thick

and that overlies a marly limestone. The limestones

dip to the southeast at about 13, though the dip

steepens near the several faults that are present.

Flow was on the strike to the southwest. There is a

major strike-oriented passage that descends from

F1 to the Deep Zone, which is up to 415m below

the former water table, and then rises to

Fitzlischacht, which is close to the former spring

(Jeannin et al., 2000). Four passages in

Siebenhengste Cave descend downdip to depths of

200300m below the former water table where they

join the main strike-aligned conduit. The nearby

cave A2 has a similar pathway.

The two flow paths shown in Fig. 9 are close to

the ideal situation of a single loop below the water

table, as shown in Figures 6b and 7b. However,

these two examples may not be representative, and

further examples are given below.

Six cave profiles are shown in Fig. 12. These

examples were chosen because they all havesubstantial maximum depths of flow below the

water table. This makes comparison to the

examples in Figures 6 and 7 simpler than for caves

developed closer to the water table. In explaining

the section of cave shown in Fig. 12a, Waltham and

Brook (1980) wrote:

If the horizontality of the trunk passage was due

to the influence of the original water table, there

seems no reason why the cave should have

developed 50 metres below water level

(Waltham and Brook, 1980, p.131).

Waltham and Brook made similar comments on

Benarat Walk (Fig. 12b), and concluded:

it is clear that the caves of Mulu must

contribute data to any thoughts on cave

genesis..... The great horizontal or sub-

horizontal phreatic tubes mostly have an

uncertain relationship to their contemporary

water table, and raise questions on the

distinction between shallow and deep phreatic

cave development (Waltham and Brook, 1980,

p.138).

The same occurrence of horizontal passages deep

below the water table is seen in Nettlebed Cave

(Figures 12c and 13) and Yorkshire Pot (Fig. 12d),

both of which, like the Mulu examples, have flow

along the strike in steeply dipping carbonates. At

Nettlebed, flow in the Oubliette was along the

strike of steeply-dipping fractures in marble (Fig.

13). At the Meltdown, the flow rose up at least 70m

in an almost circular phreatic tube (Fig. 12c). In

Yorkshire Pot, both the Roller Coaster and its

tributary, Alberta Avenue, were formed along thestrike of a steeply-dipping bedding plane in

limestone.


10/19


Fig.12.Profiles of conduits formed well below the watertable. A) Clearwater Cave, Malaysia; B) Tiger FootCave, Malaysia; C) Nettlebed Cave, New Zealand; D)Yorkshire Pot, Canada; E) Doux de Coly, France; F)

West Kingsdale System, England. (A and B afterWaltham and Brook, 1980; C after Pugsley, 1979; Dafter Worthington, 1991; E after EKPP, 2004; F adapted

from Brook and Brook, 1976 and Monico, 1995).

The situations at Doux de Coly and WestKingsdale are somewhat different because theconduits have formed along a number of bedding

planes. Flow at Doux de Coly is along the strike ofthe limestone, which has a dip of 6 (Fig. 12e).Flow below the water table in the West KingsdaleSystem is updip (Fig. 12f). The conduit may have

been formed up to 60m below the water table(Waltham, 1974) or at only 20m below the watertable (Brook, 1974). Deep flow along horizontal

passages 60m or more below the water table inYorkshire has also been described for Duke Streetin Ireby Fell Cavern (Waltham, 1974) and forSleets Gill Cave (Waltham et al.,1997).

Fig.13. Large phreatic tube in Nettlebed Cave, NewZealand. The flow from this phreatic passage ascended

more than 80m at the Meltdown (photo by C. Pugsley).

The uncertain relationship to the contemporary

water tablenoted by Waltham and Brook (1980,

p.138) for the Mulu phreatic tubes also applies to

the other caves in Fig. 12. These phreatic tubes

most closely resemble the situation in Figures 6b

and 7b, though not as well as Dent de Crolles and

Siebenhengste (Fig. 9). This suggests that the initial

flow field has had a powerful influence onsubsequent cave formation in all these examples.

Data on phreatic looping below the water table

may also be assessed by measuring the ratio of the

depth of the crests to the depth of the bases of

phreatic loops (i.e. Dc/Dbin Fig. 14). For instance,

the mean depth below the water table of loop crests

and loop bases is 35m and 58m, respectively for the

conduit in Figure 14a, and so the crest/base ratio

(Dc/Db) is 0.60. For the similarly curving flow

paths in Figures 6b, 7b, 9a and 9b the crest/base

ratios are 0.52, 0.82, 0.45 and 0.77, respectively.On the other hand, the crest/base ratios are much

smaller where the loop crests are close to the water

table: 0.18 in Fig. 14b, 0.21 in Fig. 6c, 0.36 in Fig.

7c, and 0.28 in Fig. 9 of Ford and Ewers (1978).

Loop crest/base ratios for 12 sumps and for 8

fossil passages are given in Tables 1 and 2,

respectively. The mean ratio of these twenty

examples is 0.48. This high value is similar to the

examples in Figures 9 and 12, and suggests that

there is a tendency for the depth of phreatic

conduits to be strongly influenced by hydraulic

factors that cause loop crests to be well below the

water table.


11/19


TABLE 1 Depth of the crests and bases of phreatic loops in 12 sumps

Cave Length(m)

Maximumdepth(m)

Loop crestmean depth

(m)

Loop basemean depth

(m)

Loopcrest/base

ratio

Number ofloop crestsand bases

Reference

Doux de Coly, France 5675 63 29 42 0.69 13 Figure 12e

Grotte de la Mescla,France

1510 95 30 59 0.51 18 Tardy, 1990a

Rinquelle, Germany 930 23 10.8 21.2 0.51 21 Farr, 2000

Grotte de Paques, France 810 50 4.8 19.6 0.24 11 Tardy, 1990b

Source du Lison, France 802 29 7.7 16.2 0.48 14 Isler, 1981

Joint Hole, England 700 19 3 12 0.21 11 Monico, 1995

Fontaine de SaintGeorge, France

1520 76 5 15 0.33 15 Farr, 2000

Fontaine de Ressel,France

1865 81 19 37 0.56 12 Farr, 2000

Chaudanne Spring,Switzerland

608 140 43 59 0.69 17 Farr, 2000

Btterich Spring,Switzerland

374 79 16 53 0.42 6 Farr, 2000

Blautopf, Germany 1250 24 10 17 0.53 25 Farr, 2000

Source de Bestouan 2955 29 5.6 18 0.31 14 Douchet, 1992

TABLE 2 Depth of the crests and bases of phreatic loops for 8 former conduit flow paths.

Cave Length(m)

Maximumdepth

(m)

Loop crestmean depth

(m)

Loop basemean depth

(m)

Loopcrest/base

ratio

Number ofloop crests

and bases

Reference

Roller Coaster,

Yorkshire Pot, Canada522 58 33 42 0.78 12 Figure 12d

Grotte Annette - Trou de

Glaz, France1600 79 27 60 0.45 18 Figure 9a

Ogof Hesp Alyn, Wales 1100 59 6 28 0.21 12 Appleton, 1989

Rseau de Foussoubie,France

9000 130 68 77 0.89 80 Le Roux, 1989

Wookey Hole, England 1300 95 21 37 0.65 34 Farr, 2000

Rats Nest Cave, Canada 900 136 57 82 0.69 16 Yonge, 2001

Grand Circle - BowlingAlley, Cueva del Agua,Spain

1400 206 72 106 0.78 20 Smart, 1984

Big Rift - Hole in the

Wall, Cueva del Agua,Spain

1200 104 65 83 0.77 27 Smart, 1984


12/19


TABLE 3 Structural and flow characteristics for 20 conduit flow paths (partly after Worthington, 2001)

No. Cave Geological age

Flow pathlength (m)

Stratal dip(degrees)

Range ofelevation

(m)

Mean flowdepth (m)

1 Jordtulla, Norway Palaeozoic 520 25 30 92 Otter Hole, Wales Palaeozoic 3500 6 140 10

3 Friars Hole System, West Virginia Palaeozoic 11000 2.2 200 17

4 Ogof Ffynnon Ddu, Wales Palaeozoic 3100 12 350 35

5 Doux de Coly, France Mesozoic 13700 6 200 43

6 Hlloch, Switzerland Mesozoic 11000 16 1670 100

7 Nettlebed, New Zealand Palaeozoic 7000 50 1200 120

8 Lubang Benarat, Malaysia Cainozoic 7000 45 1600 150

9 Siebenhengste, Switzerland Mesozoic 12000 13 1630 230

10 Mammoth Cave, Kentucky Palaeozoic 2200 0.6 155 2

11 Horseshoe Bay Cave, Wisconsin Palaeozoic 3000 2 30 6

12 West Kingsdale System, England Palaeozoic 2700 3 130 35

13 Rio Encantado, Puerto Rico Cainozoic 9500 4 260 15

14 Ogof Hesp Alyn, Wales Palaeozoic 2000 14 80 24

15 Guanyan, China Palaeozoic 6500 7 130 25

16 Swildons-Wookey, England Palaeozoic 3500 15 176 40

17 Trou de Glaz, France Mesozoic 1500 17 730 67

18 Pea Colorada, Mexico Mesozoic 12000 40 1760 120

19 Nelfastla de Nieva, Mexico Mesozoic 7400 70 1000 240

20 Edwards Aquifer, Texas Mesozoic 180000 1.3 160 600

Fig.14.Phreatic flow paths with (A) asingle loop deep below the water tableand (B) with loop crests just below the

water table.


13/19


Spacing of conduit-guiding bedding planes

Frequently, cave development occurs

preferentially on a limited number of bedding

planes, as noted above for the Friars Hole System,

Castleguard Cave and the Dent de Crolles System.

Lowe (2000b) described the preferential cavedevelopment in the Yorkshire Dales along just a

few bedding planes, which he called inception

horizons, and he discussed possible reasons why

just a few bedding planes in a sequence are

favoured for cave development.

It is likely that the presence of a limited number

of inception horizons in an aquifer has only a

marginal influence on the depth of flow. For

instance, there are five major cave-guiding bedding

planes in the 190m section of limestone in which

the predominantly downdip Grotte Annette to Troude Glaz passage is formed (Fig. 9a). If there were

fewer or more major cave-guiding bedding planes

in this section then the magnitude of the phreatic

lifts would change, but the cave would still be able

to follow a looping flow path that descends some

80m below the water table.

The number of cave-guiding bedding planes is

also likely to have little influence on the depth of

flow where flow is on the strike, such as at Friars

Hole System (Fig. 4), Siebenhengste (Fig. 9b), or

Mulu (Fig. 12a, 12b). In each case many bedding

planes in the dipping limestone intersect the watertable and cave passages are able to follow a single

favourable bedding plane for substantial distances.

On a particular bedding plane, the conduit is

formed at a hydraulically favourable location. This

may be just below the water table (e.g. Cleaveland

Avenue, Mammoth Cave: Palmer, 1981), 10m

below the water table (e.g. Friars Hole System: Fig.

4), 100m below the water table (e.g. Mulu: Figure

12a,b) or hundreds of metres below the water table

(e.g. Siebenhengste: Fig. 9b).

Topography

Caves in mountainous areas tend to have deep

flow paths, and several examples were noted above.

These areas also tend to have steep stratal dips and

large vertical ranges between the highest recharge

points and spring elevations. The reasons why steep

dips are associated with deep flow have been

explained earlier. But the extent to which flow

paths deep below the water table might be

associated with mountainous topography is less

clear. This is because the increase in fractureapertures in the early stages of karstification results

in a large drop in hydraulic gradients and a vadose

zone that may be more than 2000m thick, as at

Krubera Cave in Georgia (Klimchouk et al.,2004).

If flow depth below the water table is a function of

pre-karstification hydraulic gradients, then

mountainous topography could be an important

factor in promoting deep flow. On the other hand,

depth of flow may be related more to the low and

stable hydraulic gradients that exist following the

early stage of karstification. Numerical modelling

has demonstrated the rapid decline in hydraulic

gradients in the early stages of karstification and so

the steep early gradients may have little effect on

later conduit development (Gabrovek and

Dreybrodt, 2001; Kaufmann, 2002). These ideas are

tested using empirical data in the next section.

Discussion and conclusions

Discussion above of the factors influencing depth

of flow suggests that deep flow is associated with

longer flow paths, steeper dips, the presence of

open joints and faults, and possibly with a large

range in elevation in an aquifer. The four variables,

depth of flow, flow path length, stratal dip and the

range in elevation, can reasonably be estimated for

a number of aquifers (Table 3). Worthington (2001)

listed the first 19 examples shown in Table 3 and

the remaining example is the aquifer associated

with Comal Spring in Texas, which is the largest

spring in the southwest USA. A recent numericalmodel of the aquifer feeding this spring includes a

140km-long conduit that is up to 1200m below the

potentiometric surface (Lindgren et al.,2004).

Whereas it is straightforward in many cases to

evaluate flow path length, stratal dip and the range

in elevation for a karst drainage basin, there is no

simple way to evaluate fracture anisotropy.

Conduits are developed on joints or at bed/joint

intersections in most structural settings, with

platform carbonates such as at Mammoth Cave

being a notable exception. The latter also have lowdips, and so stratal dip may act as a proxy measure

of fracture anisotropy. Fig. 15 shows the

relationship between depth of flow and flow path

length, stratal dip and the range in elevation for the

examples in Table 3. Regression of mean depth of

flow against the different parameters in Fig. 15

gives:

D = 0.053 L0.77 (3)

D = 120 "0.56

(4)

D = 0.60 E0.74

(5)

D = 0.061 L0.91

"0.72

(6)

D = 0.016 L054

E0.56

(7)


14/19


D = 1.6 E0.64

"0.72

(8)

D = 0.047 L0.85

"0.64

E0.11

(9)

where D is the mean conduit depth in metres below

the water table, L is the flow path length in metres,

" is the dimensionless stratal dip (equal to the sine

of the dip in degrees), and E is the elevationdifference in metres between the lowest spring and

the highest recharge point to the aquifer. The

correlation coefficients of the above seven

equations are 0.64, 0.50, 0.68, 0.90, 0.80, 0.70 and

0.90, respectively. Equation 6, which uses length

and dip, gives the best correlation. The addition of

elevation as a dependent variable (Equation 9) does

not improve the correlation. The correlation using

length and dip can also be expressed as

D = 0.18 (L ")0.81

(10)

This equation has a lower correlation (0.79) than

Equation 6 but is simpler to express graphically

with a best-fit line added (Fig. 15d). These results

show that the two parameters of stratal dip and flow

path length explain most of the variability in

conduit flow depth.

The relationships that are apparent in Fig. 15 can

be further tested by comparing pairs of caves from

one area where the dip or flow path length varies

between the two caves. The caves of the Alyn

Gorge in Wales provide one such pair. Ogof Hen

Ffynhonau and Ogof Hesp Alyn are adjacent caves

with parallel flow routes. The latter lies further

from the adjacent valley floor and has a deeper

phreatic origin (Waltham et al.,1997). The deeper

flow in Ogof Hesp Alyn is explained by the longer

flow path (Equations 6 and 10).

Fig.15.Correlation of conduit depth of flow below the water table with A) flow path length (top left); B) Stratal dip (topright); C) Range in elevation between recharge and spring (bottom left) and D) flow path length and dip (bottom right).

Details of the 20 examples are given in Table 3.


15/19


The model presented above differs significantly

from the Ford and Ewers (1978) model, which

relates depth of flow to fissure frequency. The

fissure frequency model attributes the occurrence of

shallow or deep phreatic cave formation solely to

the degree of fracturing. The model has been

widely quoted in the literature, but suffers from

three major problems. First, the model is based on

the premise that shallow flow is the hydraulically

most favoured pathway for conduit development,

but Worthington (2001) showed that hydraulic

factors favour deep flow in most karst aquifers (see

Figure 1). The second problem is the lack of

examples that fit the model and the many examples

that contradict the model. For instance,

mountainous areas typically have both substantial

fracturing and deep flow, which is the opposite of

the prediction of the model (Rossi et al., 1997;Jeannin et al., 2000). Conversely, limestones with

little fracturing such as at Mammoth Cave and

elsewhere in Kentucky have shallow flow, which

again is the opposite of the model prediction. The

third problem is that it appears that the hypothesis

cannot be tested because Ford (2000) noted that the

model does not provide predictions. If a model

cannot provide predictions then it cannot be shown

to have any applicability.

Fig. 16 gives a summary of how hydraulic and

geological factors may interact. Figure 16a shows a

limestone aquifer with a caprock such as shale. A

simplifying assumption is made that the caprock

has recently been eroded away from the limestone.

Recharge is from a stream flowing off the caprock

as well as from precipitation onto the limestone

itself. The horizontal distance in the figure is in the

range of several to several tens of kilometres. The

vertical distance is in the range of several tens to

several hundreds of metres, so there is substantial

vertical exaggeration in the figure.

Fig. 16b shows flow lines in the limestone

immediately after the removal of the caprock. If the

limestone aquifer is of Palaeozoic age, then it is

well-lithified, the porosity is up to a few percent,

and most of the permeability is due to flow along

bedding planes, joints and faults. The combinedmatrix and fracture hydraulic conductivity in such

an aquifer is typically 10-6

10-5

m/s (Worthington

et al.,2000). Most of the recharge to the aquifer is

assumed to be from the sinking stream, and so most

of the flow lines emanate from the stream reach

where it is sinking. Discharge from the aquifer

occurs as a seepage zone in a valley.

Fig.16.Factors influencing the initial conduit flow path in a limestone aquifer: A) geological contacts and location of

valleys; B) initial flow field; C) theoretical flow path; D) actual flow path, following open fractures downdip and upjoints.


16/19


The duration of the phase shown in Fig. 16b is

extremely short (a few thousand years) because

dissolution of bedrock fractures results in the

formation of a conduit network that connects the

recharge to the discharge area. The diagnostic

features to differentiate the Figure 16c situation

from that of Figure 16b in the field are the presence

of discharge from discrete springs rather than from

dispersed seepage, as well as the low hydraulic

gradient. The low gradient is due to the increase in

permeability, which is commonly two to three

orders of magnitude (Worthington et al.,2000). A

series of simplified flow lines is shown in Figure

16b. The actual flow lines are less regular because

they follow fractures, with the enlarged pathways

being known as channels (Glennie, 1954) or

primary tubes (Ford and Williams, 1989, p.253).

Preferential enlargement of the channel that has themost favourable position and/or largest aperture

results in the conduit shown schematically in Figure

16c. The most favourable depth for channel

enlargement is a result of the balance between the

competing factors of decreasing fracture aperture

with depth and decreasing viscosity with depth; the

former promotes shallow flow and the latter

promotes deep flow. Equations 6 and 10 give

approximations of the depth below the water table

at which the conduit develops.

Fig. 16d shows a simplified scheme of the actual

conduit flow path along fractures. In reality, caves

typically follow individual joints for a few metres

to a few tens of metres, and follow individual

bedding planes for a few metres up to a few

thousand metres. Consequently, many more

fractures could be utilised than are shown in the

figure.

The question was posed earlier as to why there

are systematic differences between the shallow

phreatic caves that occur in Kentucky, deeper

phreatic caves in England, and much deeper

phreatic caves that are common in mountainousareas. Equations 6 and 9 provide the answers. The

Kentucky aquifers have shallow flow because of

the platform setting, resulting in low dips and low

permeability along joints. This is demonstrated by

the small amount of passage development along

joints and faults. Limestone aquifers in England

have deeper flow because of the structural setting,

resulting in steeper dips, open joints, many faults,

and the concomitant cave development along joints

and faults as well as along bedding planes.

Mountainous areas commonly have even deeper

flow because of a combination of open joints, steepdips and long flow paths.

Most conduit development in England is limited

to a depth of about 100m because most flow paths

are generally only a few kilometres long. From

Equation 6 or Equation 10, the deepest flow is

predicted to occur where there are steep dips and

long flow paths. The Mendip Hills have steep dips

and the Cheddar and Wookey Hole catchments are

the longest in the Mendips, and so should have the

deepest flow. The conduits feeding these spring are

likely to descend to depths greater than 100m

below the water table. Scuba diving has so far

reached a depth of -58m at Cheddar and -70m at

Wookey Hole and both conduits continue at depth

beyond the limit of exploration (Farr, 2000).

Similar conduit depths could occur along

mineralised faults in Derbyshire such as on New

Rake between P8 and Speedwell or on Faucet Rake

between P9 and Speedwell (Gunn, 1991). Evendeeper conduits may have formed in the Peak

District along long regional flow paths which

emerge at thermal springs (Worthington and Ford,

1995).

The model predicts that very deep flow is likely

at major springs, which typically have long

groundwater catchments. Mante Spring (Mexico)

and Vaucluse Spring (France) are two prominent

examples. These springs have been explored by

scuba diving or submersible vehicles to depths in

excess of 250m below the water table. Fish (1977)

concluded that the flow path to Mante Spring issome 200km long and has a maximum depth of

flow in excess of 1500m. The depth and length of

the flow system feeding Comal Spring in Texas,

which was described above, are of similar

magnitude to those of the flow system feeding

Mante Spring. Vaucluse Spring is the largest spring

in France and its groundwater catchment is more

than 60km long.

The model is applicable to most unconfined

limestone aquifers and thus to most known caves

and most limestone aquifers used for water supply.Its applicability in confined aquifers is limited

because the depth of flow may be constrained by

the structure. For instance, Bath Hot Springs are

thought to be fed by geothermally-heated water

flowing through a deep syncline (Waltham et al.,

1997, p.267). The model also does not apply to

caves formed in special situations such as hypogene

caves and sea coast mixing zone caves (Ford and

Williams, 1989, 282291).

The combination of flow path length and stratal

dip (Equations 6 and 10) together with fracture

anisotropy provide a satisfactory approximation

that explains the depth of conduit flow in areas

where the flow is at shallow depths below the water


17/19


table (e.g. Kentucky), at moderate depths (e.g.

England, Appalachian Mountains), or at great

depths (e.g. many mountainous areas and major

springs).

Acknowledgements

I wish to thank Derek Ford, who encouraged and

supported my karst research in widely diverse

geographical settings, and whose Natural Sciences

and Engineering Council of Canada research grants

supported the early part of my research while I

undertook graduate studies at McMaster University.

I am grateful to Marcus Buck for his critical

comments on an early draft, and to David Lowe and

Marcus Buck for useful comments on a later draft

of the manuscript.

References

Appleton P. 1989. Limestones and caves of North

Wales. 217254 inFord, T D (Ed.) Limestones

and caves of Wales. Cambridge: Cambridge

University Press.

Audra P. 2004. Dent de Crolles Cave System,

France. 283285 inGunn, J (Ed.) Encyclopedia

of caves and karst science. New York: Fitzroy

Dearborn.

Berner R. A. and Morse J. W. 1974. Dissolutionkinetics of calcium carbonate in sea water, IV,

Theory of calcite dissolution. American Journal

of Science, Vol.274, 108134.

Bgli A. 1964. Mischungkorrosion ein Beitrag

zum Verstrkungsproblem. Erdkunde, Vol.18,

8392.

Brook D. B. 1974. Cave development in Kingsdale.

310334 inWaltham, A C (Ed.),Limestone and

caves of north-west England. Newton Abbot:

David and Charles.

Brook D and Brook A. 1976. The West Kingsdale

System. Leeds: University of Leeds

Speleological Association.

Chabert C. 1977. Grandes cavits mondiales.

Supplement to Spelunca, No.2, 64pp.

Coase A. and Judson D. 1977. Dan yr Ogof and its

associated caves. Transactions of the British

Cave Research Association, Vol.4, 247344.

Culver D. C. and White W. B. 2005. Encyclopedia

of caves, Burlington, MA: Elsevier Academic

Press. 640pp.Davis W. M. 1930. Origin of limestone caverns.

Bulletin of the Geological Society of America,

Vol.41, 475628.

Deike G. H. III. 1989. Fracture controls on conduit

development. 259292 in White W. B. and

White E. L. (Eds), Karst hydrology: concepts

from the Mammoth Cave area.New York: Van

Nostrand Reinhold.

Douchet M. 1992. La rivire souterrain deBestouan. Spelunca, No.47, 1115.

Drew D. P. 1975. The caves of Mendip. 214312 in

Smith D. I. (Ed.) Limestone and caves of the

Mendip Hills Newton Abbot: David and

Charles.

Dreybrodt W. 1990. The role of dissolution kinetics

in the development of karst aquifers in

limestone: a model simulation of karst

evolution.Journal of Geology, Vol.98, 639655.

Dreybrodt W. 1996. Principles of early

development of karst conduits under natural andman-made conditions revealed by mathematical

analysis of numerical models. Water Resources

Research, Vol.32, 29232935.

EKPP (European Karst Plain Project). 2004. Survey

of Doux de Coly.www.ekpp.org.

Elliott J. V., Westlake C. F. and Tringham M. E.

1979. Otter Hole, near Chepstow, Wales.

Transactions of the British Cave Research

Association, Vol.6, 143158.

Farr M. 2000. The darkness beckons London:

Diadem 280pp. plus 32pp. addendum.

Fish J. E. 1977.Karst hydrogeology of Valles San

Luis Potosi region, Mexico. Unpublished PhD

thesis, McMaster University, 469pp.

Ford D. C. 1968. Features of cavern development in

central Mendip. Transactions of the Cave

Research Group of Great Britain, Vol.10, 11

25.

Ford D. C. 1971. Geologic structure and a new

explanation of limestone cavern genesis

Transactions of the Cave Research Group of

Great Britain, Vol.13, 8194.

Ford D. C. 2000. Discussion of Jeannin, P-Y,

Bitterli, T and Huselmann, P. 2000. Genesis of

a large cave system: case study of the North of

Lake Thun System (Canton Bern, Switzerland),

346 inKlimchouk, A B, Ford, D C, Palmer, A N

and Dreybrodt, W (Eds) Speleogenesis,

Evolution of karst aquifers.Huntsville, National

Speleological Society.

Ford D. C. and Ewers R. O. 1978. The development

of limestone cave systems in the dimensions of

length and depth. Canadian Journal of EarthScience,Vol.15, 17831798.


18/19


Ford D.C. and Williams P.W. 1989. Karst

geomorphology and hydrology.London: Unwin

Hyman. 601pp.

Ford D.C, Lauritzen S-E. and Worthington S.R.H.

2000. Speleogenesis of Castleguard Cave,

Rocky Mountains, Alberta, Canada, 332337 inKlimchouk A. B., Ford D.C., Palmer A.N. and

Dreybrodt W. (Eds) Speleogenesis, Evolution of

karst aquifers. Huntsville: National


Ford T. D. 1977. Limestone and caves of the Peak

District.Norwich, Geo Books. 469pp.

Gabrovek F. and Dreybrodt W. 2001. A model of

the early evolution of karst aquifers in limestone

in the dimensions of length and depth. Journal

of Hydrology, Vol.240, 206224.

Gunn J. 1991. Water tracing experiments in theCastleton Karst, 19501990. Cave Science,

Vol.18, 4346.

Gunn J. 2004. Encyclopedia of caves and karst

scienceNew York: Fitzroy Dearborn. 902pp.

Herman J.S., and White W. B. 1985. Dissolution

kinetics of dolomite: effects of lithology and

fluid flow velocity. Geochimica et

Cosmochimica Acta, Vol.49, 20172026.

Howard A.D. 1964. Processes of limestone cave

development. International Journal of

Speleology, Vol.1, 4760.

Isler O. 1981. La source du Lison, Doubs.

Spelunca, No.4, 3839.

Jameson R.A. 1985. Structural segments and the

analysis of flow paths in the North Canyon of

Snedegars Cave, Friars Hole Cave System, West

Virginia.Unpublished MS thesis, West Virginia

University, Morgantown, 421pp.

Jeannin P-Y., Bitterli T. and Huselmann P. 2000.

Genesis of a large cave system: case study of the

North of Lake Thun System (Canton Bern,

Switzerland). 338347 in Klimchouk A. B.,Ford D.C., Palmer A.N. and Dreybrodt W.

(Eds), Speleogenesis, Evolution of karst aquifers

Huntsville: National Speleological Society.

Kaufmann G. 2002. Karst aquifer evolution in a

changing water table environment. Water

Resources Research, Vol.38,

10.1029/2001WR000256.

Klimchouk A., Kasjan Y. and Solovjev N. 2004.

Arabika Massif, Western Caucasus: October

2004 expedition news. www.speleogenesis.info

Le Roux 1989. Rseau de Foussoubie, France.

Detailed plan and profile of the cave.

Lindgren R.J., Dutton A.R., Hovorka S.D.,

Worthington S.R.H. and Painter S. 2004.

Conceptualization and simulation of the

Edwards Aquifer, San Antonio Region, Texas,

U.S. Geological Survey, Scientific

Investigations Report 20045277.

Lismonde B. 1997. La Dent de Crolles et son

rseau souterrain. Comit dpartemental de

splologie de lIsre, 304pp.

Lismonde B. and Marchand T. 1997. Observations

gologiques lintrieur du rseau souterrain

217219 in Lismonde B. (Ed.), La Dent de

Crolles et son rseau souterrain. Comit

dpartemental de splologie de lIsre.

Lowe D.J. 2000a. Development of speleogenetic

ideas in the 20th Century: the early modern

approach. 3038 in Klimchouk A. B., FordD.C., Palmer A.N. and Dreybrodt W. (Eds),

Speleogenesis, Evolution of karst aquifers.


Lowe D. J. 2000b. Role of stratigraphic elements in

speleogenesis: the speleoinception concept. 65

76inKlimchouk A. B., Ford D.C., Palmer A.N.

and Dreybrodt W. (Eds), Speleogenesis,

Evolution of karst aquifers.Huntsville: National


Lowe D.J. and Gunn J. 1986. Caves and limestones

of the islands of Tongatapu and Eua, Kingdom

of Tonga. Cave Science, Vol.13, 105130.

Madelaine E. 2001. World cave database. www-

sop.inria.fr/agos-sophia/sis/DB/database.html.

Monico P. 1995. Northern sump index. Cave

Diving Group, 286pp.

Palmer A.N. 1975. The origin of maze caves.

National Speleological Society Bulletin, Vol.37,

5676.

Palmer A.N. 1981.A geological guide to Mammoth

Cave National Park. Teaneck, New Jersey:

Zephyrus Press. 196pp.

Palmer A.N. 1987. Cave levels and their

interpretation. National Speleological Society

Bulletin, Vol.49, 5066.

Palmer A.N. 1989a. Stratigraphic and structural

control of cave development and groundwater

flow in the Mammoth Cave region. 293316 in

White, W B and White, E L (Eds) Karst

hydrology: concepts from the Mammoth Cave

area. New York: Van Nostrand Reinhold.

Palmer A.N. 1989b. Geomorphic history of the

Mammoth Cave System. 317337 inWhite, WB and White, E L (Eds) Karst hydrology:


19/19


concepts from the Mammoth Cave area. New

York: Van Nostrand Reinhold.

Palmer A.N. 1991. Origin and morphology of

limestone caves. Geological Society of America

Bulletin, Vol.103, 121.

Palmer R.J. 1986. Hydrology and speleogenesisbelow Andros Island. Cave Science, Vol.13, 7

12.

Plummer L.N., and Wigley T.M.L. 1976. The

dissolution of calcite in CO2-saturated solutions

at 25C and 1 atmosphere total pressure.

Geochimica et Cosmochimica Acta, Vol.40,

191202.

Pugsley C. 1979. Caves of the Mount Arthur

region, New Zealand. Caving International,

No.4, 310.

Rossi C., Cortel A. and Arcenegui R. 1997.Multiple paleo-water tables in Agujas Cave

System (Sierra de Pealabra, Cantabrian

Mountains, N Spain): criteria for recognition

and model for vertical evolution. 183186 in

Proceeding of the 12th International Congress

of Speleology, Vol. 1La Chaux-de-Fonds: Swiss


Sasowsky I. and White W.B. 1994. The role of

stress-relief fracturing in the development of

cavernous porosity in carbonate aquifers. Water

Resources Research,Vol.30, 35233530.Smart P.L. 1984. The geology, geomorphology and

speleogenesis of the Eastern Massifs, Picos de

Europa, North Spain. Cave Science, Vol.11,

238245.

Swinnerton A.C. 1932. Origin of limestone

caverns. Bulletin of the Geological Society of

America, Vol.43, 663694.

Tardy J-C. 1990a. Siphon de la Mescla, Malaucne.

Spelunca, No.40, 45.

Tardy J-C. 1990b. Siphon de Paques; rsurgence de

la Foux, Saint-Czaire. Spelunca, No.40, 56.

Thrailkill J. 1968. Chemical and hydrologic factors

in the excavation of limestone caves. Geological

Society of America Bulletin, Vol.79, 1946.

Waltham A.C. 1974.Limestone and caves of north-

west England. Newton Abbot: David and

Charles. 477pp.

Waltham A.C. and Brook D.B. 1980.

Geomorphological observations in the limestone

caves of the Gunung Mulu National Park,

Sarawak. Transactions of the British Cave

Research Association,Vol.7, 123139.

Waltham A. C. and Hatherley P. 1983. The caves ofLeck Fell. Transactions of the British Cave

Research Association, Vol.10, 245247.

Waltham A.C., Simms M.J., Farrant A.R. and

Goldie H.S. 1997. Karst and Caves of Great

Britain, London: Chapman and Hall. 358pp.

Weyl P.K. 1958. The solution kinetics of calcite.

Journal of Geology, Vol.66, 163176.

White W.B. 1988. Geomorphology and hydrology

of karst terrains.New York: Oxford University

Press. 464pp.

Worthington S.R.H. 1984. The paleodrainage of anAppalachian fluviokarst: Friars Hole, West

Virginia. Unpublished MSc thesis, McMaster

University, 218pp.

Worthington, S R H. 1991. Karst hydrogeology of

the Canadian Rocky Mountains. Unpublished

PhD thesis, McMaster University, 380pp.

Worthington S.R.H. 2001. Depth of conduit flow in

unconfined carbonate aquifers. Geology,Vol.29,

335338.

Worthington S.R.H. and Ford D.C. 1995. High

sulfate concentrations in limestone springs: an

important factor in conduit initiation?

Environmental Geology, Vol.25, 915.

Worthington S.R.H., Ford D.C. and Beddows P.A.

2000. Porosity and permeability enhancement in

unconfined carbonate aquifers as a result of

solution. 463472 in Klimchouk A. B., Ford

D.C., Palmer A.N. and Dreybrodt W. (Eds),

Speleogenesis, Evolution of karst aquifers


Worthington S.R.H. and Medville D.M. 2005.

Friars Hole Cave System, West Virginia. 264270 in Culver, D C and White, W B (Eds),

Encyclopedia of caves. Burlington, MA:

Elsevier Academic Press. 640pp.

Yonge C.J. 2001. Under Grotto Mountain; Rats

Nest Cave. Calgary: Rocky Mountain Books.

144pp.

worthington, stephen r. h. hydraulic and geological factors influencing conduit flow depth

Documents